Spatially Resolved Spectroscopy

Nuclear magnetic resonance has been successfully used in biomedicine for imaging and in vivo spectroscopy. However, both NMR modes have been severely limited by the availability of excitation selective only for simple shapes, eg. spherical, cylindrical, or cubic volumes. We developed new excitation excitation sequence selective for Completely Arbitrary Regional Volume Excitation (CARVE). CARVE sequence can be used for high resolution NMR spectroscopy and volume-selective imaging of precisely delineated organs, tumors, body parts, etc.

To design a desired excitation profile, we chose a sequence of short, small-flip-angle RF pulses in combination with the constant linear arbitrarily orientable gradient. The desired excitation profile resulted from a sequence of N constant intervals, with small-flip-angle pulses, their phases and the associated gradients. The gradients were constant within intervals, but were different between the intervals. Likewise, the tilt angles and the phases of RF pulses differed between the intervals.

CARVE excitation sequence and corresponding k-space trajectory for the 'A' shaped profile with 100 excitation events.

The application of the completely arbitrary regional volume excitation (CARVE) in a on resonance spin-system, encompasses three steps. First, all coefficients for the desired excitation profile in the k-space are found by nD Fourier transformations (FT) of the excitation profile, and the N largest complex coefficients are retained together with the respective k-vectors k. Second, the tip angles and RF phases are calculated from the Fourier coefficients. The vectors k are constant and need be visited only once during the excitation sequence. In contrast to the continuous k-space analysis, the order of visitation is not important, but different pathways may require different gradient strengths. The best path to visit N vectors k is the one with minimum required gradients and minimum gradient switching. Consequently, in the third step, the optimal path is found by the use of simulated annealing and by minimizing the sum of squares of individual gradient pulses.

The process of CARVE sequence calculation: ideal excitation profile, its transformation into k-space, selection of 100 coefficients with the highest amplitude and the expected profile after the excitation sequence.

During the CARVE sequence magnetization is subjected to rotations by RF pulses toward or away from the z-axis and rotations by the gradient steps around the z-axis. Because gradient rotation is spatially dependent every magnetization component has different trajectory during the sequence but at the end of the sequence all components within the profile realign along the y-axis and outside the profile are restored back along z- axis. This is illustrated in the figure below where typical trajectories within and outside the excitation profile are shown. The arrows in the figure a) show the position of the magnetization components for which the trajectories are shown in b). Within the profile, the magnetization components are aligned such that majority of the RF pulses tip them from the z-axis, (b, left). At the same time the components outside the profile are randomly tipped toward and away from the z-axis so that the net effect is no tilt at all, (b right).

Magnetization trajectory during CARVE sequence for a point within the profile (left) and out of it (right).

Experimental verification. cylindrical tube filled with water (left) and measured excited 'A' shaped profile in the same tube with the CARVE sequence (right).

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